Finding Angles and Their Relationships

The video tutorial explains how to find the smallest four positive radian solutions for the equation 5 sin(π/3x) = 1. It involves substituting θ = π/3x, solving for θ using a calculator, and identifying solutions in the first and second quadrants. The tutorial then calculates the corresponding X values by multiplying θ by 3/π, ensuring results are rounded to three decimal places.

What is the initial substitution made to simplify the equation 5 sin(π/3x) = 1?

• Theta = x/π

• Theta = π/3x

• Theta = 3/πx

• Theta = 5/πx

Which function is used to find the value of theta when sin(theta) = 1/5?

• Inverse Sine

• Tangent

• Inverse Cosine

• Cosine

In which quadrants is the sine function positive?

• Second and Fourth

• First and Third

• First and Second

• Third and Fourth

What is the approximate value of theta for the first solution?

• 0.3014

• 0.2014

• 0.4014

• 0.1014

How do you find the second solution for theta in the second quadrant?

• Multiply the reference angle by 2

• Subtract the reference angle from π

• Divide the reference angle by 2

• Add the reference angle to π

What is the formula to find coterminal angles?

• Multiply by π

• Add or subtract π

• Add or subtract 2π

• Divide by 2π

What is the approximate value of theta for the third solution?

• 5.4846

• 7.4846

• 8.4846

• 6.4846

What is the relationship between x and theta in the final calculation?

• x = π/3 * theta

• x = 3/π * theta

• x = θ/π

• x = 5/π * theta

What is the approximate value of x for the first solution?

• 0.492

• 0.392

• 0.292

• 0.192

What is the approximate value of x for the fourth solution?

• 8.808

• 7.808

• 9.808

• 6.808